Abstract

A direct version of the boundary element method (BEM) is developed to
model the stationary dynamic response of reinforced plate structures, such as
reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary
fundamental solutions of thin plates and plane stress state are used to transform
the governing partial differential equations into boundary integral equations (BIEs).
Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state
(membrane) and for the out-of-plane state (bending). These uncoupled systems
are joined to form a macro-element, in which membrane and bending effects are
present. The association of these macro-elements is able to simulate thin-walled
structures, including reinforced plate structures. In the present formulation, the BIE
is discretized by continuous and/or discontinuous linear elements. Four
displacement integral equations are written for every boundary node. Modal data,
that is, natural frequencies and the corresponding mode shapes of reinforced plates,
are obtained from information contained in the frequency response functions (FRFs).
A specific example is presented to illustrate the versatility of the proposed
methodology. Different configurations of the reinforcements are used to simulate
simply supported and clamped boundary conditions for the plate structures.
The procedure is validated by comparison with results determined by the finite
element method (FEM).

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